My understanding is that the "appeal to authority fallacy" is specifically about appealing to irrelevant authorities. Quoting a physicist on their opinion about a physics question within their area of expertise would make an excellent non-fallacious argument. On the other hand, appealing to the opinion of say, a politician or CEO about a physics question would be a classic example of the appeal to authority fallacy. Such people's opinions would represent expert evidence in their fields of expertise, but not outside them.
I don't think the poster's description makes this clear and it really does suggest that any appeal to authority at all is a logical fallacy.
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With a recursively self-improving AI, once you create something able to run, running a test can turn to deploying even without programmer's intention.
Even if we manage to split the AI into modules, and test each module independently, we should understand the process enough to make sure that the individual modules can't recursively self-improve. And we should be pretty sure about the implication "if the individual modules work as we expect, then also the whole will work as we expect". Otherwise we could get a result "individual modules work OK, the whole is NOT OK and it used its skills to escape the testing environment".
"escape the testing environment" is poorly defined. Some people read it as "deduce the exploitable vulnerabilities in the system, hack into it, run itself with higher privileges, somehow transmit itself to other machines / the internet at large / infecting people's brains snow-crash style", and others read it as "convince the people running the test to give it more resources (and maybe infect their brains snow-crash style)".
The former can be prevented by having a secure (air gapped?) system, the latter can be prevented by not running tests interactively and ignoring the moral issues with terminating (or suspending) what may possibly be an intelligent 'person'.
It also implicitly assumes that its ability to improve its own intelligence (and therefore gain the ability to do either of the above) is unbounded by the resources of the system and will have no cost in terms of increased processing time.